What are you talking about? The rule to choose the correct chain is well defined and simple. The longest chain, i.e. the one with the most work done, is the correct chain.
Some developers would agree with you though, like Gavin Andresen [0].
Either way, you end up with either centralized miners deciding the fate of the chain, or centralized developers deciding the fate of the chain. Both outcomes are contrary to what Satoshi envisioned.
Useless pedantry that doesn't even map into real world use. The real world has shown your definition is incorrect.
Ethereum forked. Which ethereum fork is the "correct" one? Bitcoin forked. Which one is the correct one? Depends on who you ask...
My understanding is that the danger of miner control is not "double-spending" but making multiple spends and being able to pick the most favorable one after the fact.
As a non-controller if you try to double-spend, you can't know which one of your attempted transactions will be recorded in the ledger and which will be rejected. As a 51% controlling miner, you can choose the 'correct' transaction.
This allows the 51% controlling miner to engage in futures arbitrage.
If it wasn't clear, my comment was referring to a double-spend that would result in an invalid block i.e. both transactions are on the same chain. I simply used an example to argue that it's always been the case that invalid chains are rejected by honest nodes.
Taken to the logical conclusion, a supernode that is issuing algorithm changes is no different from a supernode that is signing blocks directly, just vastly more inefficient. Since you are already centralized, there is no reason to have miners at all. It becomes a ponzi scheme where the rewards are paid out randomly to participants.